Let \(\lbrace \mathcal {T}_h\rbrace _h\)  be a family of conforming triangulations of \(\Omega \) , indexed by the mesh size \(h\max _{T\in \mathcal {T}_h}h_T\) , where \(h_T\)  is the diameter of the element \(T\) .
This family is assumed to be regular in the classical sense; see, e.g., [1]}.
Furthermore, each triangulation is conformal to the subdivision of the boundary into \(\Gamma _D\) , \(\Gamma _N\) , and \(\Gamma _C\)  in the sense that the interior of a boundary edge (if \(d=2\) ) or face (if \(d=3\) ) cannot have non-empty intersection with more than one part of the subdivision.
Mesh-related notations that will be used in the a posteriori error analysis are collected in Table REF .
For the sake of simplicity, from this point on we adopt the three-dimensional terminology and speak of faces instead of edges also in dimension \(d=2\) .
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